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Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…

This paper presents static and dynamic versions of univariate, multivariate, and multilevel functional time-series methods to forecast implied volatility surfaces in foreign exchange markets. We find that dynamic functional principal…

Detection of periodic patterns of interest within noisy time series data plays a critical role in various tasks, spanning from health monitoring to behavior analysis. Existing learning techniques often rely on labels or clean versions of…

By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…

Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…

I overview recent research advances in Bayesian state-space modeling of multivariate time series. A main focus is on the decouple/recouple concept that enables application of state-space models to increasingly large-scale data, applying to…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Ongoing and future surveys with repeat imaging in multiple bands are producing (or will produce) time-spaced measurements of brightness, resulting in the identification of large numbers of variable sources in the sky. A large fraction of…

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

The self-similar analysis of time series is generalized by introducing the notion of scenario probabilities. This makes it possible to give a complete statistical description for the forecast spectrum by defining the average forecast as a…

There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…

We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…

This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…

Time series forecasting is a crucial challenge with significant applications in areas such as weather prediction, stock market analysis, and scientific simulations. This paper introduces an embedded decomposed transformer, 'EDformer', for…

A robust model for time series forecasting is highly important in many domains, including but not limited to financial forecast, air temperature and electricity consumption. To improve forecasting performance, traditional approaches usually…

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of…

Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series…